What is a Risk Free Rate?

Risk-free interest rate refers to the interest rate that can be obtained by investing funds in an investment object without any risk. This is an ideal investment income. Generally affected by the benchmark interest rate. Interest rate is the compensation of opportunity cost and risk. The compensation of opportunity cost is called risk-free interest rate. Professionally speaking, it refers to the investment of assets without credit risk and market risk, which refers to the interest rate of government bonds with a maturity date equal to the investment period.

Risk-free interest rate

The risk-free rate is

Impact of risk-free interest rate on warrant price :

Factors affecting the price of warrants include not only the stock price, but also the exercise price of the warrant, the volatility of the stock price, the remaining term, and the risk-free interest rate. Among them, the first four factors have a more definite impact on the price of warrants, such as the price of the underlying stock and the price of the warrant change in the same direction and the price of the put warrant in the opposite direction; Puts) the price changes in a positive direction and so on. The impact of the risk-free interest rate on the price of warrants is more complicated. In actual situations, different conclusions will be drawn from different perspectives.

First of all, in terms of the effect of the risk-free interest rate on the price of the warrant, the impact of the risk-free rate on the price of the warrant can generally be understood as: the price of the subscription warrant will rise with the rise in the risk-free rate,

Selection of risk-free interest rates:

In countries with developed bond markets such as the United States, there are three views on the selection of risk-free interest rates:

Viewpoint 1: Use the short-term Treasury bond interest rate as the risk-free interest rate, and use the stock market historical risk premium rate of return calculated based on the short-term Treasury rate as the estimated value of the market risk premium rate of return. Based on these data, the cost of equity capital is calculated as the discount rate for future cash flows.

Example: CAPM model using spot short-term Treasury rates: PepsiCo

In December 1992, the beta value of PepsiCo was 1.06, and the short-term Treasury rate at that time was 3.35%. The cost of the company's equity capital was calculated as follows:

Cost of equity = 3.35% + (1.06 × 6.41%) = 10.14%

We can use 10.14% equity capital as a discount rate for dividends or cash flows to calculate the value of PepsiCo stock.

Viewpoint 2. Use the historical short-term government bond and market historical risk premium yield to calculate the first period (year) of the cost of equity capital. At the same time, the forward interest rate in the term structure is used to estimate the forward risk-free interest rate as the cost of equity capital in the future.

Example: CAPM model using forward interest rates: PepsiCo

Assume that the interest rate of spot government bonds is 3.35%. The one-year forward rate in the term structure of interest rates is as follows:

1-year forward interest rate = 4.0%; 2-year forward interest rate = 4.4%; 3-year forward interest rate = 4.7%; 4-year forward interest rate = 5.0%.

Use these forward rates to calculate the cost of equity capital:

Cost of equity in the first year = 3.35% + (1.06 × 6.4% 1) = 10.14%

Cost of equity in the second year = 4% + (1.06% × 6.1%) = 10.47%

Cost of equity in the third year = 4.4% + (1.06 × 5.9%) = 10.65%

Cost of equity in the fourth year = 4.7% + (1.06 × 5.8%) = 10.85%

Cost of equity in the fifth year = 5% + (1.06 × 5.7%) = 11.04%

Note: In the above calculations, the longer the period, the lower the market risk premium return. This shows that compared with the risk premium rate of return on the current Treasury bond rate, the historical risk premium rate of return on the stock market with relatively forward rate is lower.

Viewpoint 3: Use the current long-term Treasury bond interest rate as the risk-free interest rate, and use the stock market historical risk premium rate of return calculated based on the long-term Treasury rate as the estimated value of the market risk premium rate of return. Based on these data, the cost of equity capital is calculated as the discount rate for future cash flows.

Example: Use the current long-term Treasury bond rate of 7% to calculate the market's risk premium return on the basis of long-term Treasury bonds instead of short-term Treasury bonds. The market risk premium yield was 5.5% from 1926 to 1990. Given that the beta value of PepsiCo's stock is 1.06, the cost of equity capital is: Cost of equity = 7% + 1.06 × 5.5% = 12.83%

Of the three viewpoints given above, which one is the best? The viewpoint is theoretically and intuitively reasonable. The first view is that CAPM is a single-period risk-return model, and the short-term Treasury bond interest rate is a reasonable expectation of future short-term interest rates. The second view focuses on the advantages of forward interest rates in predicting future interest rates, and the third view holds that long-term Treasury bonds have the same maturity period as the valued assets.

In practice, when the term structure of interest rates is the same as the relationship between short-term and long-term interest rates in history, and the value of approaches 1, the results calculated by these three methods are the same. When the term structure deviates from the historical data, or is far from equal to 1, the results calculated by these three methods are different. If the yield curve slopes up more, then the discount rate obtained using long-term interest rates will be higher, which will cause an underestimation of value. If the yield curve slopes upwards to a lesser extent or even downwards, the conclusion is just the opposite.